Perform each calculation. See Example 3. 47° 29' ― 71° 18'

Verified step by step guidance

1. First, understand that the problem involves subtracting two angles given in degrees and minutes: \(47^\circ 29'\) and \(71^\circ 18'\). Since the second angle is larger, the result will be negative, but we will proceed with the subtraction process as usual.
2. Convert the minutes part of the angles to a common base and subtract the minutes: subtract \$18'\( from \)29'$. If the top minutes are smaller than the bottom minutes, borrow 1 degree (which equals 60 minutes) from the degrees part before subtracting.
3. Subtract the degrees: after adjusting for any borrowing, subtract \(71^\circ\) from \(47^\circ\). Remember to account for the borrowing done in the previous step.
4. Combine the results of the degrees and minutes subtraction to express the answer in degrees and minutes format.
5. Since the second angle is larger, the final answer will be negative. Express the result with a negative sign to indicate this.

Key Concepts

Degrees, Minutes, and Seconds in Angle Measurement

Angles can be expressed in degrees (°), minutes ('), and seconds ("), where 1 degree equals 60 minutes and 1 minute equals 60 seconds. Understanding this notation is essential for performing arithmetic operations on angles accurately.

Subtraction of Angles in DMS Format

When subtracting angles given in degrees, minutes, and seconds (DMS), you must subtract each component separately, borrowing from higher units if necessary (e.g., borrowing 1 degree as 60 minutes) to avoid negative values in minutes or seconds.

Conversion Between Units for Simplification

To simplify calculations, angles in DMS can be converted to decimal degrees or all to seconds before performing arithmetic, then converted back to DMS. This method helps avoid errors and makes subtraction straightforward.